I've been considering shapes formed when we take $n$-tuple such as $\{0,1,2\}$ and plot all permutations forming a shape (for $n=2$ its a line, for $n=3$ it's a hexagon). However I'm having trouble trying to understand the plot for $n=4$, mainly because it's in 4D and that's hard to plot. I feel as though it's just going to make $n!$-polygon. I'm in high school so I don't really have a rigorous mathematical training hence why I'm looking for some guidance in how to approach such problems.

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    $\begingroup$ It seems to me that you are rediscovering this construction: en.wikipedia.org/wiki/Permutohedron Cool :-) $\endgroup$ – Lorenzo Mar 28 at 21:49
  • $\begingroup$ Oh thanks I was just thinking about ways of making the superpermutations problem geometric so it's nice that people have thought of this before. $\endgroup$ – John Miller Mar 28 at 21:50

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